You need level 30 Archer and level 15 Pugilist to unlock Bard.
However, since you stated that you dislike Bard, you may want to find a different job that you enjoy more.

With regards to classes, most groups will not be happy seeing a level 60 Archer in their group, even if you are a stellar archer. At level 30, it is expected of everyone to transfer from being a class into a job.
So, if Bard is not the job for you, then you should look for something that you think you would enjoy more (even though Bard is still an Archer, just with songs and a couple more abilities). I would urge you to at least give Bard a try, if you have never played it in a FFXIV setting.